Afootball is thrown upward at a 31° angle to the horizontal. the acceleration of gravity is 9.8m/s^2. to throw the ball a distance 77 m, what must be the initial speed of the ball. answer in units of m/s

The ball's vertical position in the air at time is

The ball is at its original height when , which happens at

Meanwhile, the ball's horizontal position at time is

So when the ball reaches its original height a second time, the ball will have traveled a horizontal distance of

(which you might recognize as the formula for the range of a projectile)

To reach a distance of , the initial speed would be

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